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TECHNICAL BRIEFS

An Explicit Minimum-Time Solution for the Simple Harmonic Oscillator

[+] Author and Article Information
Slim Choura, Suhada Jayasuriya

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123

J. Dyn. Sys., Meas., Control 112(4), 783-787 (Dec 01, 1990) (5 pages) doi:10.1115/1.2896210 History: Received May 12, 1989; Online March 17, 2008

Abstract

It is well known that the minimum time control of a simple harmonic oscillator subjected to a bounded control input is a bang-bang control where the input cannot remain constant for more than half of the period of the oscillator. The necessary switching times for implementing such bang-bang control are usually determined by geometric means in the state-space, thus making it difficult to obtain the switchings and the final time for an arbitrary initial condition. An explicit solution for the switching times and the final time for a motion starting from an arbitrary initial state subjected to an arbitrary but constant input bound is developed for the simple harmonic oscillator. The explicit solution matches exactly the graphical solution (Athans and Falb, 1966).

Copyright © 1990 by The American Society of Mechanical Engineers
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